Thermoelectric properties of Yb$_{14}$MnSb$_{11}$ from first-principles*

The complex Zintl compound, Yb$_{14}$MnSb$_{11}$, has been recently given much attention as a high-performance thermoelectric due to its nearly twice the figure of metrit ($zT$) of p-type SiGe at high temperatures ( $>$ 900K)\footnote{S. R. Brown et al., Chem. Mater. {\bf 18}, 1873 (2006)}. Its high $zT$ can be attributed to low lattice thermal conductivity combined with a large Seebeck coefficient ($S$) and high electrical conductivity ($\sigma$) at high temperatures. To understand the thermoelectric properties of Yb$_{14}$MnSb$_{11}$ and to find possible improvements for thermoelectric performance, we have investigated its electronic structures and electrical transport properties ($S$,$\sigma$) using the highly precise FLAPW method\footnote{Wimmer, Krakauer, Weinert, Freeman, Phys. Rev. B {\bf 24}, 864 (1981)} with the local spin density approximation (LSDA) and LSDA+U\footnote{Shick et al, Phys. Rev. B {\bf 60}, 10763, (1999)} methods. We have found significantly different spin moments of Mn between the LSDA and the LSDA+U methods. Also, we determined the anisotropy of the conductivity. The linear temperature behavior of the Seebeck coefficients will be discussed from and related to the electronic structures.